Sigma-Delta ADC Tutorial and Latest Development in 90 nm … · 2005. 6. 27. · Sigma-Delta ADC Tutorial and Latest Development in 90 nm CMOS for SoC Jinseok Koh Wireless Analog

Sigma-Delta ADC Tutorial and Latest Development in 90 nm

CMOS for SoC

Jinseok KohWireless Analog Technology Center

Texas Instruments Inc. Dallas, TX

Outline

• Fundamentals for ADCs

• Over-sampling and Noise shaping

• Sigma-Delta ADC

• Double Sampling Technique

• 2nd Order Single Amplifier Sigma-Delta ADC

• Implementation in 90nm CMOS for SoC

• Conclusions

1

Modeling of Quantizer

• Quantizer is non-linear building block– Need modeling for simplifying the analysis

• White additive noise assumptions– It is not fulfilled in many applications, However– It makes analysis easy and makes possible the use of z-tansformation

2

Quantization Noise

• Quantity of in-band noise depends on the over-sampling ratio– SNR = 10log(σx

2) -10log(σn2) +3.01r(dB), where

– σx2 and σn

2 are input signal power and in-band noise power respectively, and

– r is defined by over-sampling ratio, fs/2fb=2r

Pervez M. Aziz, “An overview of sigma-delta converters,” IEEE Signal processing Magazine, pp 61-84, Jan. 1996

3

Nyquist Rate vs. Oversampled

FsSignal Band Fs/2

Anti-Aliasing FilterDigital Filter

Any unwanted signals Fs/2 to Fs are folded into band of 0 to Fs/2

4

Over-sampling and Noise Shaping

fs 2fs 4fs

Band of Interest

Noise

fs 2fs 4fs

Noise

Every doubling of sampling frequencyleads approximately 3 dB enhancement in SNR

Noise shaping pushes quantization noise to higher frequency resulting in suppressing Q. noise in the band of interest

5

How to Shape the noise?

E(z)H(z)G(z)1

1X(z)H(z)G(z)1H(z) Y(z) ⋅

++⋅

+=

If H(z) = z-1/1-z-1 and G(z)=1, NTF and STF will be:

STF NTF

1ZX(z)Y(z)STF −==1Z1

E(z)Y(z)NTF −−==

6

Example, 2nd order Sigma-Delta ADC

7

Summary

• Sigma-delta ADC provide trade-offs between:– Power consumption,– Over-sampling ratio (OSR)– System performance (SNR)

• High OSR implies:– Lower number of quantization levels – Lower modulator order, but– More demanding settling requirements for the analog

building blocks

8

Objectives

• For a given performance requirement, power consumption and area are optimized by: – Increasing sampling frequency Double sampling technique– Increasing modulator order Single Amplifier topology– Higher number of levels in Quantizer 5-level quantizer with

ILA

9

Double sampling

• Advantages:– Efficient technique to double the OSR

• Doesn’t need faster op-amp settling • Provides improvement of SQNR by 6n+3 dB (n=order)

• Disadvantage: – Mismatch between capacitors creates noise folding

inP1

P1

P1

P1

P2

P2

P2

P2

D1

D2

u

Inherent Capacitor Mismatch

Alternating Gain Effect

Noise Folding

10

Noise Folding In Double Sampling• Alternating gain effect

Noise at Fs/2 is folded into Signal bandwidth

D2CΔC:gain

1:gain

Noise folding (Input sampling circuit)

Noise folding(DAC in feedback path)

D2CΔC:gain

1:gain

• Noise at Fs/2 is suppressed by- Anti-aliasing filter- Pre-filtering

• No filtering on quantization noise

11

VrefpP1

P2

CD1

CD1

CD2

CD2

Vrefm

SA

SB

SB

SA

SA

SB

SB

SA

P1

P1

P1

P1

P1

P2

P2

P2

P2

P2

CU

CU

Conventional Double Sampling DAC

• Requires two sets of switched capacitor DACs

• Mismatch on stored charge causes alternating gain effect

• On P1 phase,Stored charge in CD1 :CD1(Vrefp-Vrefm)

• On P2 phase,Stored charge in CD2 :CD2(Vrefp-Vrefm)

12

• Advantages of this approach vs. conventional approach:– Only one pair of capacitors needed– No “alternating-gain” effect– No additional circuitry needed for matching purposes

Proposed SC DAC element for double sampling

13

• On phase P1 the charge transferred to Integrating Capacitor is:– Qu = Cd(Vrefp-Vrefm)– Qu is equal to the charge stored into Cd– This charge will be used during next integration phase

Operation of Proposed SC DAC element

On P1 Phase: On P2 Phase:

14

b 1 b 2

• Conventional Sigma-delta ADC:– Needs an amplifier per summing node– Poles and zeros are chosen by ai and bi ,where i=1,2

Conventional 2nd Order Sigma-Delta ADC

15

Each Summing Node requires an Amplifier

G(z)1z2zq1zp1

2zq1zp1NTF−+−⋅−−⋅−

−⋅−−⋅−=G(z)zzqzp1

zSTF 121

1

−−−

−

+⋅−⋅−=

Summing node

Single Amplifier 2nd Order Sigma-Delta ADC

16

Q-path OperationH(z): Forward path Filter

p

z-1

z-1

q

p-path

q-path

• Rotating to do sampling, holding and integrating functions– The first SC circuit samples the output vo(n)

– while the second one holds the previous output vo(n-1)

– and the third one transfers vo(n-2) to the integrating capacitor, CU

q1

q2

q3

U

P5 P5

P3

P3 P3

P5

P4

P4

P4P4 P5

P3

17

Full Filter implementation

18

Amplifier design (SR, GBW)

• GBW and SR were simulated in Matlab behavioral model • Amplifier was designed to have:

- DC Gain>60dB, SR>100V/µsec and GBW > 50MHz• Single amplifier topology has a benefit since settling requirement

is lower than conventional one

SNR vs. Amplifier DC gain

40

45

50

55

60

65

70

35 45 55 65 75Gain [dB]

SNR

[dB

]

x107

19

SNR vs. GBW (SR=100V/usec)

585960616263646566676869

0.2 0.4 0.6 0.8 1 1.2GBW [Hz]

SNR

[dB

]

Amplifier implementation

Load Capacitance 1.6 pFGBW 100 MHzInput referred Noise* 70 uVrmsSlew Rate 200 V/usecCurrent Consumption 700 uA

20

Pow

er S

pect

ralD

ensi

ty [d

B]

Frequency [Hz]

WCDMA BAND1.94MHz

Measured Power Spectral Density

• Input signal: -6 dBFS sine at 448 kHz• 3rd harmonic shows up at -91 dBV

• Noise floor shows no noticeable noise folding21

SNDR vs. Input

0

10

20

30

40

50

60

70

-70 -60 -50 -40 -30 -20 -10 0

Input Amplitude [dBFS]

SND

R [d

B]

SNDR vs. Input power

• 63dB peak SNDR happens at -3dBFS input sinusoidal

22

I-channel Q-channel

Die Photography for dual channel ADCs

23

• Implemented in 90nm 5 metal digital CMOS process

Technology 90 nm Digital CMOSSignal Bandwidth 1.94 MHzClock Frequency 38.4 MHz

Sampling Frequency 76.8 MHzPeak SNDR 63 dB

Dynamic Range 66 dBInput Range 1.5 Vpp (differential)

Voltage Supply 1.2 VPower Consumption 1.2 mW per ADC

Core Area 0.2 mm2 per ADC

Performance Summary

24

Conclusions

• Second order 5 level Single Amplifier Sigma-Delta ADC with double sampling technique was realized in 90 nm CMOS.

• By using double sampling technique, OSR is doubled with no increase of power consumption and silicon area.

• Single-capacitor double-sampling DAC solved “alternating-gain” error effect.

• 2nd order modulator is implemented using a Single-amplifier architecture. Higher order modulator is feasible.

• Low power consumption: 1.2mW for WCDMA, measured with a 1.2V power supply.

• 66dB dynamic range was achieved in 1.94MHz bandwidth.

25